Contracted horns with least mouth reflection and some wall leakage



March 23, 1965 SEIICHI KOJIMA 4 3 174 578 CONTRACTED HORNS WITH LEAST MOUTH REFLECTION AND SOME WALL. LEAKAGE Filed Sept. 27, 1962 X ae 2 /7 .20 L

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INVENTOR SEIICHI KOJIMA ATTORNEY United States Patent 3,174,578 CONTRACTED HORNS WITH LEAST MOUTH REFLECTION AND SOME WALL LEAKAGE Seiichi Kojima, 483 Iwato Komae-machi, Kita-Tama-gun, Tokyo, Japan Filed Sept. 27, 1962, Ser. No. 226,689 Claims priority, application Japan, Oct. 6, 1961, 36 36,332 1 Claim. (Cl. 181-27) This invention relates to contracted horns having minimum reflection of sound at the mouth of the horn and some wall leakage.

In the accompanying drawings FIG. 1 represents a longitudinal section of the device constructed in accordance with my invention and FIG. 2 is a graph showing the output pressure response for a horn embodying the invention.

The embodiment of this invention shown in the drawings will now be described in detail.

The horn 1 of FIG. 1 has innumerable pores or slits in the wall 2, which pores are arranged near the mouth portion as described hereinafter. Air is allowed to leak through the pores or slits and is damped by acoustical resistance 3 such as silk cloth or wire gauze stretched over the pores or slits.

The sound wave travelling from the horn throat 4 is initially a plane wave 5 and gradually changes to a spherical wave 6 as it passes the region where the wall has pores or slits. The change in shape of the sound wave results from the fact that the horn tends to have the character of the open end of an acoustical tube at the portion of the horn having pores owing to the leakage through the wall and the wave at the open end assumes the form of spherical Wave as is well known.

Upon reaching the horn mouth 7 the sound wave surface can take the form of a sphere 8 whose radius is almost equal to that of the horn mouth if suitable leakage through the wall is allowed. If the radius of the sound wave at 8 is equal to the radius of the horn mouth 7, the sound wave does not reflect at the horn mouth and the output sound pressure of the horn has no peak nor dip at varying frequencies.

According to the theory explained hereinafter, the necessary mouth radius of the born to satisfy this condition is just half of that of the usual horn. As is well known, the usual horn with a small mouth radius has a bad he quency characteristic owing to the reflection of the sound wave at the horn month which is caused by the difference between the radius of the spherical sound wave at the mouth of the horn and the radius of the horn mouth itself.

On the other hand, if leakage through the mouth portion of the wall of the horn is selected in accordance with this invention, horns or apparatus with relatively small mouths, but with excellent frequency characteristics can be made. The tweeter and squawker horns embodying this invention have wider directional characteristics owing to the relatively smaller horn mouths as compared with conventional ones; while woofer horns embodying this invention have more convenient dimensions and weights for domestic use. For example, the usual Woofer horns must have mouth dimension of 2 m. x 2 m. in order to truly reproduce bass tones of 50 cycles per second and to maintain an even frequency characteristic.

3,174,578 Patented Mar. 23, 1955 Further, the so-called horn bafiie is also reduced in size for a horn embodying this invention.

The theory of this invention will now be explained briefly with reference to an exponential horn as follows:

Differentiating by time the condensation of the air contained in the increment of volume 9 at the section 11 having a cross-sectional area S and thickness Ax in FIG. 1, and multiplying by p6 we get the sound pressure p:

where Now velocity potential gives sound pressure p= 9/6t and particle velocity u=68x as usual; then Formula 1 leads to equations E 9i 2 ,+m +(k .7 2)

G=2pg /(1/R) +(m/2) 3) where k=w/c, w=angular frequency of sound and j= /1.

The solution Ct of the Equation 2, when G=constant, is

and

i gwmm] where The acoustical impedance density of this horn is, then,

The output sound wave at the horn mouth is nearly a spherical wave, the radius of which is almost equal to the 3 radius of the horn mouth; and the impedance density at the mouth is, therefore, nearly equal to where r=radius of horn mouth; this computation is well known in the acoustical engineering of usual or conven tional horns.

The condition for avoiding reflection of the sound wave at the horn mouth is, then,

referring to Equation 6, then, we can derive the conditional equations r l/m (mouth radius) (9) G m/c (constant) hence g c /l+(mR/2) (10) hence According to Equation 9, the radius of the horn embodying this invention has a size of .l/m, which is just half the size of the mouth radius of the usual horn. To obtain a good response from this half-sized horn over its reproducing frequency range, however, the Equation 10 must be satisfied. In Equation 10 g means the acous tical leakage conductance per unit area of the wall and it will be seen that change in g along the horn is almost proportional to the change in R (the radius of the cross section of the horn); hence the area of the wall made up (mouth radius of the usual horn) of the pores or slits is to be nearly proportional to R.

It is desirable that the horn wall have no leakage near its throat, but getting near the mouth, the wall gradually permits sound leakage in accordance with Equation 10, in order to avoid unnecessary loss of sound power; and the leakage conductance must be almost real, that is, purely frictional, rather than inertial or elastic conductance, in order to obtain the desired condition over the reproducing frequency range.

One of the invented hornspeakers, the response of which is observed by a Briiel & Kjaers apparatus and is shown in FIG. 2, has a mouth area of about 230 cm. and approximate low and high cutoff frequencies of 320 c./s. and 3000 c./s. respectively. Its response, which rises 6 db per octave in the lower range owing to the small size of the mouth but has no conspicuous peak nor dip, can easily be compensated by a conventional tone controlling device.

This invention is also applicable to all other shapes of horns such as conical or hyperbolic horns as well as to the exponential horn of the particular example.

What I claim is:

A contracted horn including a wall flaring from a throat to a mouth with a flaring constant m, the radius of the horn at said mouth being equal to approximately l/m, the portion of said wall of the horn adjacent said mouth having openings therein and acoustical resistance material covering said openings to provide a varying damped leakage conductance therein of approximately PG 1/1+ mR/ per unit area at any point along said portion of the wall, in which p is the mean density of air, c is the velocity of sound and R is the cross-sectional radius of the horn at said point, thereby to ensure minimum mouth reflection.

References Cited by the Examiner UNITED STATES PATENTS 1,840,992 1/32 Weitling 18127 2,621,261 12/52 Karlsson et al l8l-3l X FOREIGN PATENTS 844,769 5/39 France. 600,150 7/34 Germany.

22,965 12/08 Great Britain. 491,510 7 9/38 Great Britain.

LEO SMELOVV, Primary Examiner.

C. W. ROBINSON, Examiner. 

